Results 1  10
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17
A module calculus for Pure Type Systems
, 1996
"... Several proofassistants rely on the very formal basis of Pure Type Systems. However, some practical issues raised by the development of large proofs lead to add other features to actual implementations for handling namespace management, for developing reusable proof libraries and for separate verif ..."
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Cited by 23 (3 self)
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Several proofassistants rely on the very formal basis of Pure Type Systems. However, some practical issues raised by the development of large proofs lead to add other features to actual implementations for handling namespace management, for developing reusable proof libraries and for separate verification of distincts parts of large proofs. Unfortunately, few theoretical basis are given for these features. In this paper we propose an extension of Pure Type Systems with a module calculus adapted from SMLlike module systems for programming languages. Our module calculus gives a theoretical framework addressing the need for these features. We show that our module extension is conservative, and that type inference in the module extension of a given PTS is decidable under some hypotheses over the considered PTS.
A Calculus of Substitutions for IncompleteProof Representation in Type Theory
, 1997
"... : In the framework of intuitionnistic logic and type theory, the concepts of "propositions" and "types" are identified. This principle is known as the CurryHoward isomorphism, and it is at the base of mathematical formalisms where proofs are represented as typed lambdaterms. In ..."
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Cited by 18 (1 self)
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: In the framework of intuitionnistic logic and type theory, the concepts of "propositions" and "types" are identified. This principle is known as the CurryHoward isomorphism, and it is at the base of mathematical formalisms where proofs are represented as typed lambdaterms. In order to see the process of proof construction as an incremental process of term construction, it is necessary to extend the lambdacalculus with new operators. First, we consider typed metavariables to represent the parts of a proof that are under construction, and second, we make explicit the substitution mechanism in order to deal with capture of variables that are bound in terms containing metavariables. Unfortunately, the theory of explicit substitution calculi with typed metavariables is more complex than that of lambdacalculus. And worse, in general they do not share the same properties, notably with respect to confluence and strong normalization. A contribution of this thesis is to show that the pr...
Pure type systems in rewriting logic
 In Proc. of LFM’99: Workshop on Logical Frameworks and MetaLanguages
, 1999
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Perpetual Reductions in λCalculus
, 1999
"... This paper surveys a part of the theory of fireduction in λcalculus which might aptly be called perpetual reductions. The theory is concerned with perpetual reduction strategies, i.e., reduction strategies that compute infinite reduction paths from λterms (when possible), and with perpetual r ..."
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Cited by 8 (0 self)
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This paper surveys a part of the theory of fireduction in λcalculus which might aptly be called perpetual reductions. The theory is concerned with perpetual reduction strategies, i.e., reduction strategies that compute infinite reduction paths from λterms (when possible), and with perpetual redexes, i.e., redexes whose contraction in λterms preserves the possibility (when present) of infinite reduction paths. The survey not only recasts classical theorems in a unified setting, but also offers new results, proofs, and techniques, as well as a number of applications to problems in λcalculus and type theory.
Typechecking Injective Pure Type Systems
, 1993
"... Injective Pure Type Systems form a large class of Pure Type Systems for which one can compute by purely syntactic means two sorts elmt(\GammajM ) and sort(\GammajM ), where \Gamma is a pseudocontext and M is a pseudoterm, and such that for every sort s, \Gamma ` M : A \Gamma ` A : s ) elmt(\Gamm ..."
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Cited by 5 (1 self)
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Injective Pure Type Systems form a large class of Pure Type Systems for which one can compute by purely syntactic means two sorts elmt(\GammajM ) and sort(\GammajM ), where \Gamma is a pseudocontext and M is a pseudoterm, and such that for every sort s, \Gamma ` M : A \Gamma ` A : s ) elmt(\GammajM ) = s \Gamma ` M : s ) sort(\GammajM ) = s By eliminating the problematic clause in the (abstraction) rule in favor of constraints over elmt(:j:) and sort(:j:), we provide a sound and complete typechecking algorithm for injective Pure Type Systems. In addition, we prove Expansion Postponement for a variant of injective Pure Type Systems where the problematic clause in the (abstraction) rule is replaced in favor of constraints over elmt(:j:) and sort(:j:). 1
Pure type systems in rewriting logic: Specifying typed higherorder languages in a firstorder logical framework
 In Essays in Memory of OleJohan Dahl, volume 2635 of LNCS
, 2004
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The SemiFull Closure of Pure Type Systems
 Proceedings of MFCS’98, volume 1450 of Lecture Notes in Computer Science
, 1998
"... We show that every functional Pure Type System may be extended to a semifull Pure Type System. Moreover, the extension is conservative and preserves weak normalization. Based on these results, we give a new, conceptually simple typechecking algorithm for functional Pure Type Systems. 1 ..."
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Cited by 4 (1 self)
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We show that every functional Pure Type System may be extended to a semifull Pure Type System. Moreover, the extension is conservative and preserves weak normalization. Based on these results, we give a new, conceptually simple typechecking algorithm for functional Pure Type Systems. 1
Dependent Types and Explicit Substitutions
, 1999
"... We present a dependenttype system for a #calculus with explicit substitutions. In this system, metavariables, as well as substitutions, are firstclass objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization. ..."
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Cited by 3 (0 self)
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We present a dependenttype system for a #calculus with explicit substitutions. In this system, metavariables, as well as substitutions, are firstclass objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization.
Pure type systems with more liberal rules
 Journal of Symbolic Logic
"... Pure type systems with more liberal rules Pure Type Systems. PTSs, introduced as a generalisation of the type systems of Barendregt's lambdacube, provide a foundation for actual proof assistants, aiming at the mechanic verification of formal proofs. In this paper we consider simplifications of ..."
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Pure type systems with more liberal rules Pure Type Systems. PTSs, introduced as a generalisation of the type systems of Barendregt's lambdacube, provide a foundation for actual proof assistants, aiming at the mechanic verification of formal proofs. In this paper we consider simplifications of some of the rules of PTSs. This is of independent interest for PTSs as this produces more flexible PTSlike systems, but it will also help, in a later paper, to bridge the gap between PTSs and systems of Illative Combinatory Logic. First we consider a simplification of the start and weakening rules of PTSs. which allows contexts to be sets of statements, and a generalisation of the conversion rule. The resulting Setmodified PTSs or SPTSs, though essentially equivalent to PTSs, are closer to standard logical systems. A simplification of the abstraction rule results in Abstractionmodified PTSs or APTSs. These turn out to be equivalent to standard PTSs if and only if a condition (*) holds. Finally we consider SAPTSs which have both modifications.